The layered organic superconductors kappa-(BEDT-TTF)(2)X exhibit similar normal and superconducting state properties with those of the high temperature cuprate superconductors. Many experimental measurements support the version that the superconducting state is on the verge of the Mott insulator. Using the strong-coupling approach, we employ the Gutzwiller variational method to study a two-dimensional Hubbard model including a spin exchange coupling term on an anisotropic triangular lattice as a minimal model for the compounds. The ground state is found to be a Gossamer superconductor at a small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. The lattice structure anisotropy, or the ratio of the hopping integrals along different lattice orientation t'/t plays an important role in determining the highly non-trivial phase diagram. Our theory is qualitatively consistent with major experiments reported in organic superconductors.